Y. S. Muzychka

Thermal Spreading Resistance of Eccentric Heat Sources on Rectangular Flux Channels

A general solution, based on the separation of variables method for thermal spreading resistances of eccentric heat sources on a rectangular flux channel is presented. Solutions are obtained for both isotropic and compound flux channels. The general solution can also be used to model any number of discrete heat sources on a compound or isotropic flux channel using superposition. Several special cases involving single and multiple heat sources are presented. @DOI: 10.1115/1.1568125#

Spreading Resistance of Isoflux Rectangles and Strips on Compound Flux Channels

The general expression for the spreading resistance of an isoe ux, rectangular heat source on a two-layer rectangular e ux channel with convective or conductive cooling at one boundary is presented. The general expression depends on several dimensionless geometric and thermal parameters. Expressions are given for some two- and three-dimensional spreading resistances for two-layer and isotropic e nite and semi-ine nite systems. The effect of heat e ux distribution over strip sources on two-dimensional spreading resistances is discussed. Tabulated values are presented for three e ux distributions, the true isothermal strip, and a related nonisoe ux, nonisothermal problem. For narrow strips, the effect of the e ux distribution becomes relatively small. The dimensionless spreading resistance for an isoe ux square source on an isotropic square e ux tube is discussed, and a correlation equation is reported. The closed-form expression for the dimensionless spreading resistance for an isoe ux rectangular source on an isotropic half-space is given.

Laminar forced convection heat transfer in the combined entry region of non-circular ducts

A new model for predicting Nusselt numbers in the combined entrance region of non-circular ducts and channels is developed. This model predicts both local and average Nusselt numbers and is valid for both isothermal and isoflux boundary conditions. The model is developed using the asymptotic results for convection from a flat plate, thermally developing flows in non-circular ducts, and fully developed flow in non-circular ducts. Through the use of a novel characteristic length scale, the square root of cross-sectional area, the effect of duct shape on Nusselt number is minimized. Comparisons are made with several existing models for the circular tube and parallel plate channel and with numerical data for several non-circular ducts

Modeling friction factors in non-circular ducts for developing laminar flow

Solutions to hydro dynamically developing flow in circular and non-circular ducts are examined. It is shown that the apparent friction factor based upon the square root of the crosssectional area is a weak function of the shape of the geometry provided an appropriate aspect ratio is defined. A general model which is valid for many duct configurations is developed by combining the developing flow and fully developed flow asymptotes. The new model is simpler than other general models and provides equal or better accuracy. Finally, it is shown that the solution for the elliptic duct geometry may be used to compute accurately, results for 8 singly-connected ducts and 2 doubly-connected ducts, respectively, with an accuracy of ±12 percent.

Thermal Spreading Resistance in Compound and Orthotropic Systems

Ar eview of thermal spreading resistances in compound and orthotropic systems is presented. Solutions for thermal spreading resistances in compound systems are reported. Solutions are reported for both cylindrical and rectangular systems, variable flux distributions, and edge cooling. Transformations of the governing equations and boundary conditions for orthotropic systems are discussed, and new solutions are obtained for rectangular flux channels and circular flux tubes. Nomenclature Ab = baseplate area, m 2 Am, An, Amn, Bn =F ourier coefficients As = heat source area, m 2 a, b

Computational Fluid Dynamics Study for Flow of Natural Gas through High-pressure Supersonic Nozzles: Part 1. Real Gas Effects and Shockwave

Abstract The computational fluid dynamics technique was used to study the behavior of high-pressure natural gas in supersonic nozzles. Although many applications of gas flow produce insignificant errors when the gas is assumed ideal, our results indicate significant variation of gas properties. This article illustrates natural gas behavior when it is considered to be real and how erroneous the properties may become when the gas is assumed to be ideal. The article also presents the influences of properties related to the flow of natural gas through supersonic nozzles. Using a quite accurate equation of state model, real gas effects are studied and compared with the perfect gas case. The results show a significant variation in gas properties estimation. Location of shockwave is also analyzed. The comparison of results for two gases (methane and nitrogen) indicated that shockwave position can significantly change when the gas is considered as real rather than perfect.

The Influence of Material Properties and Spreading Resistance in the Thermal Design of Plate Fin Heat Sinks

The thermal design of plate fin heat sinks can benefit from optimization procedures where all design variables are simultaneously prescribed, ensuring the best thermodynamic and air flow characteristic possible. While a cursory review of the thermal network established between heat sources and sinks in typical plate fin heat sinks would indicate that the film resistance at the fluid-solid boundary dominates, it is shown that the effects of other resistance elements, such as the spreading resistance and the material resistance, although of lesser magnitude, play an important role in the optimization and selection of heat sink design conditions. An analytical model is presented for calculating the best possible design parameters for plate fin heat sinks using an entropy generation minimization procedure with constrained variable optimization. The method characterizes the contribution to entropy production of all relevant thermal resistances in the path between source and sink as well as the contribution to viscous dissipation associated with fluid flow at the boundaries of the heat sink. The minimization procedure provides a fast, convenient method for establishing the “best case” design characteristics of plate fin heat sinks given a set of prescribed boundary conditions. It is shown that heat sinks made of composite materials containing nonmetallic constituents, with a thermal conductivity as much as an order of magnitude less that typical metallic heat sinks, can provide an effective alternative where performance, cost, and manufacturability are of importance. It is also shown that the spreading resistance encountered when heat flows from a heat source to the base plate of a heat sink, while significant, can be compensated for by making appropriate design modifications to the heat sink. DOI: 10.1115/1.2429713

Influence of Geometry and Edge Cooling on Thermal Spreading Resistance

This paper presents a simple geometric transformation for predicting thermal spreading resistance in isotropic and compound rectangular flux channels using the solution for an isotropic or compound circular flux tube. It is shown that the results are valid for a wide range of channel aspect ratios and source to base coverage ratio. Because the circular disk solution requires a single series summation, it is preferable to the rectangular flux channel solution, which requires the evaluation of two single-series and one double-series summation. The effect of edge cooling is also addressed in flux tubes and flux channels. A new analytical solution is obtained for thermal spreading resistance in a rectangular flux channel with edge cooling. This solution contains many limiting cases, including a previously published solution for adiabatic edges. Comparisons are made with the circular flux tube with edge cooling and with adiabatic edges. Simple relationships are developed for edge-cooled systems to assess the importance of edge cooling. This alleviates the issue of computing or recomputing eigenvalues when the edge-cooling conditions change or have no impact. It is shown that this simple approach provides good results for a wide range of dimensionless parameters.

Computational Fluid Dynamics Study for Flow of Natural Gas through High-pressure Supersonic Nozzles: Part 2. Nozzle Geometry and Vorticity

Abstract The computational fluid dynamics technique is used to study the behavior of high-pressure natural gas when it flows through nozzles with supersonic velocities. Effect of nozzle geometry is discussed by inserting a constant area channel between the convergent and divergent parts of the system. Various conduit lengths are analyzed to show how the minimum temperature could be influenced by the geometry of the nozzle. The results also show that changing channel length can affect the position of shockwave. The results for the effect of vorticity on the performance of the nozzles show that, although losses in pressure increase due to inlet swirl flow, vorticity increases very sharply in the vicinity of the shock. It could be concluded that the region just before the shock spot is the main region where fine particles can be separated because of the large vorticity strength. Shock with reasonable strength may be favored in practical applications where fine particles separation is desired.

Thermal resistance models for non-circular moving heat sources on a half space

The analysis of heat transfer from sliding and rolling contacts is important in many tribological applications such as ball bearing and gear design. In these applications heavily loaded contacts are typical and knowledge of the contact temperatures which result from frictional heat generation is required for minimizing thermal related problems such as scoring, lubricant breakdown, and adhesive wear due to flash welding. A review of typical tribology books such as the texts by Halling @1# and Williams @2#, and Handbook sections by Winer and Cheng @3# and Cowan and Winer @4# shows that the analysis of heat transfer from sliding or rolling contacts has not been extensively modelled. These reviews generally present equations and results for only one configuration, the circular contact. Although this contact geometry arises quite frequently in tribology applications, others such as the elliptic contact are also quite common in ball bearing and gear applications where non-conforming contacts prevail @5‐7#. The analysis for moving heat sources which is presented in a number of tribology references @1‐4#, is based upon the assumption that one of the contacts can be modelled as a stationary heat source and the other as a fast moving heat source. In many problems the assumption of a fast moving heat source may not be valid and the analysis will incorrectly predict the average or maximum contact temperature. With this in mind, Tian and Kennedy @8# developed accurate correlations for the circular and square heat source which predict the temperature for any speed. These correlations were then used to formulate models for predicting flash temperatures in sliding asperities. In a recent paper @9#, a hybrid computational method for noncircular heat sources was developed. For this method, a numerical approach based upon the superposition of point heat sources was employed for the stationary portion and a transient finite element method was employed for the moving portion. This new approach was then used to predict temperatures in a steel/bronze sliding contact problem, with sliding motion normal and parallel to the grinding direction. The primary motivation for the work of Neder et al. @9# was that the conventional approach adopted in most tribology references was not applicable to non-circular heat sources. The present work discusses various aspects of heat transfer in tribological applications involving stationary and sliding contacts. In all cases heat is either supplied to the contact or is generated through contact friction. This paper has four objectives. These are ~i! provide a comprehensive review of the literature related to stationary and moving heat sources on half space, ~ii! examine the effect that heat source shape and heat flux distribution have on the thermal resistance, ~iii! develop a model which is applicable to a heat source of arbitrary shape and flux distribution, and ~iv! use the proposed model to predict the flash temperature in a noncircular contact for real surfaces. In addressing these issues, a number of gaps in the literature have been filled. In addition, a clear and consistent approach to modeling arbitrary contacts has been developed. Presently, the field of tribology has only adopted a simplified approach in the prediction of contact temperatures due to sliding. The present approach does not allow for the effect of shape, aspect ratio, and flux distribution to be modelled easily. This was the primary motivation of the development of a hybrid numerical scheme by Neder et al. @9#. The expressions and method developed in the present work have been validated against a small set of numerical data for real and ideal contacts. The results of Neder et al. @9# are readily computed using the present approach with significantly less effort.